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We present a novel direct multiway spectral clustering algorithm in the<jats:italic>p<\/jats:italic>-norm, for<jats:inline-formula><jats:alternatives><jats:tex-math>$$p\\in (1,2]$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>p<\/mml:mi><mml:mo>\u2208<\/mml:mo><mml:mo>(<\/mml:mo><mml:mn>1<\/mml:mn><mml:mo>,<\/mml:mo><mml:mn>2<\/mml:mn><mml:mo>]<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>. The problem of computing multiple eigenvectors of the graph<jats:italic>p<\/jats:italic>-Laplacian, a nonlinear generalization of the standard graph Laplacian, is recasted as an unconstrained minimization problem on a Grassmann manifold. The value of<jats:italic>p<\/jats:italic>is reduced in a pseudocontinuous manner, promoting sparser solution vectors that correspond to optimal graph cuts as<jats:italic>p<\/jats:italic>approaches one. Monitoring the monotonic decrease of the balanced graph cuts guarantees that we obtain the best available solution from the<jats:italic>p<\/jats:italic>-levels considered. We demonstrate the effectiveness and accuracy of our algorithm in various artificial test-cases. Our numerical examples and comparative results with various state-of-the-art clustering methods indicate that the proposed method obtains high quality clusters both in terms of balanced graph cut metrics and in terms of the accuracy of the labelling assignment. 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